Research Note pubs.acs.org/IECR
Experimental Research on the Power Consumption of a Coaxial Mixer in a Fluid with High Viscosity Baoqing Liu, Jingliang Liu, Yikun Zhang, Mingqiang Chen, Fulei Qin, and Zhijiang Jin* Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, People’s Republic of China ABSTRACT: The power consumption of a coaxial mixer consisting of an outer anchor and different inner impellers was experimentally characterized in an agitating vessel full of Newtonian fluids (highly viscous malt syrup). Meanwhile, taking the rotation mode, speed ratio, and diameter ratio between the inner and outer impellers into consideration, a novel correlation for the calculation of the total power consumption of the coaxial mixer was introduced by defining a new characteristic diameter and a new characteristic speed. The results show that the inner impeller has an obvious effect on the power consumption of the outer impeller: the power consumption of the outer impeller will decrease under co-rotation mode and increase under counter-rotation mode. The power consumption of the high-speed inner impeller accounts for a large percentage of the total power consumption and the outer impeller has little effect on it. Compared with other existing correlations, the Reynolds number calculated from the novel correlation is greater and the power number is smaller, which can better reflect the high efficiency and low power consumption of the coaxial mixer.
1. INTRODUCTION Agitating equipment is a type of general machinery widely used in process industries such as chemical engineering, petrochemical, pharmaceutical, food, metallurgy, and papermaking industries. During many industrial processes, the phase and viscosity will change.1 For such processes, single-shaft mixers cannot fulfill the different mixing tasks effectively, regardless of whether it uses dispersive impellers or anchor or ribbon impellers.2 Therefore, coaxial mixers, which represent a type of mixing system with wide adaptability, are developed to meet the diverse mixing requirements.3 Usually, the coaxial mixer is vertically arranged, and it has two main structures, as shown in Figure 1.4 In the first diagram, the inner and outer mixing shafts enter the vessel from the top and bottom of the tank, respectively. In the second diagram, both the inner and outer mixing shafts enter the vessel from the top of the tank. The earliest literature on the coaxial mixer was reported by Schneider from EKATO Company.5 Tanguy’s research group
from Canada then did a series of research on a type of coaxial mixer, which focused mainly on the influence of rotation modes and speed ratios on the power consumption and mixing time.6−9 In recent years, researchers in China have also done some research on coaxial mixers and made some progress.10−14 Of all the existing research on coaxial mixers, the first type of coaxial mixers shown in Figure 1(a) got most of the attention, while literature about the second type of coaxial mixers has not been reported publicly so far. Therefore, in this paper, we have studied the power characteristics of the second type of coaxial mixer, consisting of a wall-scraping anchor and three types of single-layer impellers, and proposed a novel correlation for the calculation of the total power consumption of the coaxial mixer by considering the rotation mode, speed ratio, and diameter ratio between the inner and outer impellers.
2. EXPERIMENT 2.1. Experimental Setup. The apparatus used for the experiment is shown in Figure 2. In order to observe the mixing conveniently, the stirring vessel, with an ellipsoidal head, is composed of transparent organic glass, whose diameter and height are 380 mm and 570 mm, respectively. The coaxial mixer has dual shafts that can rotate at different speeds and toward different directions at the same time. Its outer shaft is hollow, and the inner shaft is solid. To avoid radial shaking of the inner shaft and achieve sealing, a wear-resistant ring made of Teflon was embedded into the gap between the inner and outer shafts. In addition, in the experiment, the outer impeller is wall-scraping anchor constantly and is connected with the outer shaft through bolts, and a Rushton turbine, a six-straight-blade turbine (SBTReceived: Revised: Accepted: Published:
Figure 1. Diagram showing the main structures of coaxial mixers. © 2013 American Chemical Society
6862
January 21, 2013 April 2, 2013 May 8, 2013 May 8, 2013 dx.doi.org/10.1021/ie4002266 | Ind. Eng. Chem. Res. 2013, 52, 6862−6867
Industrial & Engineering Chemistry Research
Research Note
Table 1. Types and Sizes of Inner Impellers No.
type
sizea
1 2 3
Rushton turbine six-straight-blade turbine 45° six-pitched-blade turbine
d = 200, b = 40, l = 50 d = 200, b = 40 d = 200, b = 40
a
d is the impeller diameter; b is the width of the blade; and l is the blade length of the Rushton impeller.
Table 2. Physical Parameters of Malt Syrup
Figure 2. Experimental setup.
parameter
value
concentration temperature density viscosity
64 wt % 14 °C 1345 kg/m3 8.0 Pa s
M = MLoad − MIdling
(1)
P = 2πNM
(2)
Re =
ρNd 2 μ
(3)
Np =
P ρN3d5
(4)
where M is the net torque (N m), MLoad the load torque (N m), MIdling the idling torque (N m), P the power (W), Np the power number, Re the Reynolds number, N the rotation speed (revolutions per second), d the diameter of the impeller (m), ρ the density (kg/m3), and μ the viscosity (Pa s).
6 for short), and 45° six-pitched-blade turbine (45° PBT-6 for short) are used as inner impellers in turn, which are fixed to the inner shaft through the use of fastening screws. The structures and sizes of the different inner impellers are shown in Figure 3 and listed in Table1, respectively. 2.2. Experimental Materials. Nontoxic and transparent malt syrup was chosen as the Newtonian fluid in the experiment, whose viscosity was easy to adjust by changing its concentration. During the experiment, the density and rheological properties of malt syrup under experimental temperature were determined using a densitometer and digital viscometer, and its specific physical parameters are listed in Table 2. 2.3. Testing Method. During the experiment, the rotating speeds of the inner and outer impellers were controlled through frequency converters, and the torque of the inner impeller and outer impeller were measured by torque sensors. These parameters not only can be read directly from the display panel of the control cabinet, but also can be saved in real time into a database through the data acquisition card. The power consumption and power number of the inner impeller and outer impeller then were calculated using of the following formulas, in which the net torque (M) was obtained by subtracting the idling torque from the load torque:
3. RESULTS AND ANALYSIS 3.1. Effect of Inner Impeller on the Power Consumption of the Outer Impeller. Figure 4 illustrates the relationship between the power number (Np) and the Reynolds number (Re) of the outer impeller under different speed ratios (RN, which is equal to Ni/No) and rotation modes, when the corresponding inner impeller is SBT-6 and 45° PBT-6, respectively. It can be found that the power consumption of the outer impeller is largely influenced by the rotation of the inner impeller: it will increase under counter-rotation mode and decrease under co-rotation mode; in addition, the greater the RN value, the larger the magnitude of increase or decrease. This is because the rotation of the inner impeller causes the motion of the fluid, which has an effect on the anchor. It acts as a driving force under co-rotation mode and resistance under counter-rotation mode. In addition, the higher the speed of the inner impeller, the greater the force on the anchor. In addition, although the overall trend is as mentioned above, there will be
Figure 3. Structures of inner impellers: (a) Rushton turbine, (b) six-straight-blade turbine (SBT-6), and (c) 45° six-pitched-blade turbine (45° PBT6). 6863
dx.doi.org/10.1021/ie4002266 | Ind. Eng. Chem. Res. 2013, 52, 6862−6867
Industrial & Engineering Chemistry Research
Research Note
Figure 5. Power curves of the inner impeller.
Figure 4. Power curves of the outer impeller.
4. CORRELATION FOR THE CALCULATION OF TOTAL POWER CONSUMPTION OF THE COAXIAL MIXER Research on the power consumption of the single-shaft mixer has been sufficient, and there are also many correlations for the calculation of its power consumption. However, research on the total power consumption of the coaxial mixer is few, let alone the literature about the effect of different configurations of inner impeller and outer impeller on total power consumption. Compared with the conventional mixer with a single shaft, the power curve of the coaxial mixer is difficult to characterize, since the diameter and speed used to calculate the Re and Np values of the system are difficult to determine. First, there are two shafts, each equipped with an inner impeller and an outer impeller, which can rotate at different speeds and toward different directions. Moreover, the diameters of the inner impeller and the outer impeller are different, and the type and size of the inner impeller are not the same under different circumstances. The classic calculation formulas of Re and Np proposed in the past are mainly for the single-shaft mixing system, and in order to apply these classic calculation formulas to a coaxial mixing system, it is essential to equivalently transform the effect of two rotation speeds and two diameters into that of one rotation speed and one diameter. With the help of the idea of
slight fluctuations, which are mainly due to the measurement error of the torque and viscosity. 3.2. Effect of the Outer Impeller on the Power Consumption of the Inner Impeller. The power curves of the inner impeller under different speed ratios and operating modes are shown in Figure 5. As can be seen from Figure 5, under the same conditions, the power consumption of the inner impeller under counter-rotation mode is slightly higher than that under co-rotation mode, which agrees with the conclusions of Xie et al.,2 Foucault et al.,3 and Guo et al.11 Therefore, the power consumption of the inner impeller is still influenced by the outer impeller, but the effect is quite limited. The reason for this situation is that the outer impeller with large diameter mainly plays the role of scraping the wall, to promote the fluid flow near the wall of the stirring vessel. Meanwhile, the power consumption of the outer impeller accounts for a relatively small proportion of the total power consumption, because of its low rotation speed; thus, the outer impeller has little effect on the inner impeller. However, the co-rotation mode is still superior to the counter-rotation mode, from the viewpoint of power consumption. 6864
dx.doi.org/10.1021/ie4002266 | Ind. Eng. Chem. Res. 2013, 52, 6862−6867
Industrial & Engineering Chemistry Research
Research Note
4.1. Definition of Novel Correlation. Based on previous research, a new definition of the characteristic diameter is introduced first, which is defined as
equivalent transformation, the mixing effect generated by the coaxial mixing system in practice would be transformed into the effect of an equivalent single-shaft system existing in theory. Based on this idea, some scholars had tried to correct the classical calculation formulas of Re and Np to calculate the total Reynolds number and power number values of the coaxial mixing system. For the coaxial mixing system, Tanguy et al.3 introduced the concept of equivalent rotation speed first and proposed a valuable correlation. They defined the equivalent rotation speed as N = Ni ± No
⎡ ⎛ 1 ⎞⎤ D = ⎢1 + ⎜DN − ⎟⎥Di ⎢⎣ RN ⎠⎥⎦ ⎝
The characteristic diameter of a coaxial mixer is a virtual diameter similar to that of a single-shaft mixing system; that is, the power consumption of a coaxial mixer with a specific characteristic diameter is equal to that of a single-shaft mixer with the same diameter. Equation 8 shows that the characteristic diameter becomes correspondingly greater as the speed ratio RN and diameter ratio DN each increase. Then, considering the impact of rotation mode, speed ratio (RN), and diameter ratio (DN) synthetically, a novel equivalent rotation speed (which is called the characteristic rotation speed) is defined:
(5)
where N is the equivalent rotation speed, Ni the rotation speed of the inner impeller, and No the rotation speed of the outer impeller. The minus sign is adopted under co-rotation mode and the plus sign is adopted under counter-rotation mode. Equation 5 mainly takes the influence of rotation mode into account and is only applicable for RN > 10. Based on the above work, a novel formula of equivalent rotation speed then was proposed by Farhat et al.,15 based on the definition of the drag coefficient in hydromechanics, and its expression was as follows: N=
NiDi + NoDo Di
⎛ 1 1 ⎞ N = N+ ± ⎟No i ⎜ RN ⎠ ⎝ DN
No RN
(9)
where the minus sign is adopted under co-rotation mode and the plus sign is adopted under counter-rotation mode.16 Novel revised calculation formulas of the Reynolds number (Re) and power number (Np) of the coaxial mixer can be obtained by substituting the characteristic diameter and characteristic rotation speed defined above for the diameter and speed in the classical formulas of Re and Np. A summary of all the correlations for the calculation of total Reynolds number and power number of the coaxial mixing system is shown in Table 3. 4.2. Comparison and Application of Correlations for the Calculation of Total Power of the Coaxial Mixer. In order to test the rationality of the novel correlation in calculating the total power consumption of the coaxial mixer, we selected the classical Ruston turbine as the inner impeller and determined the power curves of the coaxial mixer. The power curves determined by different correlations listed in Table 3 under different rotation modes and speed ratios are shown in Figure 6. As can be seen from Figure 6: (1) All power curves have similar trends and are approximately declining lines in the double logarithmic coordinates, which coincides with the conclusions of the past research. However, the results computed from different correlations show big differences: with the same Re, Np1 > Np3 > Np2 > Np4 under co-rotation mode, while Np3 > Np1 > Np2 > Np4 under counter-rotation mode. (2) The magnitude of the difference between the Np corotation mode and the Np counter-rotation mode varies. The magnitude is the largest when using correlation 1, while it is less when adopting correlation 3 or correlation 4. (3) Because both the characteristic diameter and characteristic rotation speed calculated by method 4 are bigger compared with that by other methods, the calculated Reynolds number is larger and the power number is smaller when they were introduced into correlation 4, which leads the power curve calculated from correlation 4 to lie in the lower right part of the coordinate.
(6)
where Di is the diameter of the inner impeller and Do is the diameter of the outer impeller. Xie et al.2 proposed another expression of equivalent rotation speed, according to the effect of operation mode and speed ratio (RN), on the basis of experimental study:
N = Ni ±
(8)
(7)
where the minus sign is adopted under co-rotation mode and the plus sign is adopted under counter-rotation mode. From what have been shown above, we can see that, in the previous research, the effects of the diameters of the inner and outer impellers were not fully taken into account in the calculation of Re and Np of the coaxial mixing system. But, in fact, they are not negligible. First of all, let us see the impact of the diameter of the outer impeller. Supposing that there is no outer impeller, highly viscous fluid in the near-wall region of the stirring vessel is rather difficult to be driven with a single inner turbine impeller. In contrast, fluid in the region relatively far from the center of the vessel can be mixed well when the outer impeller rotates with the inner impeller. The influence of the diameter of the inner impeller on power consumption and mixing performance then is analyzed. Usually, the flow field in a vessel equipped with a coaxial mixer is mainly controlled by the high-speed inner impeller. Hence, the diameter of the inner impeller has an important effect on the range of fluid flow. In general, the higher the viscosity of materials in the stirring vessel, the larger the diameter of the inner impeller should be, to effectively overcome the viscous resistance of fluid. In other words, the larger the diameter of the inner impeller and the higher its rotation speed, the larger the affected range of the inner impeller and the more violent the fluid in the vessel moves, which is beneficial for avoiding the dead zone of mixing. Therefore, the diameter ratio (DN, which is defined as DN = Di/ Do) should also be taken into account in the calculation of total power consumption of the coaxial mixing system. 6865
dx.doi.org/10.1021/ie4002266 | Ind. Eng. Chem. Res. 2013, 52, 6862−6867
4
3
2
1
No.
3
this paper
Xie et al.2
Farhat et al.15
Foucault et al.
author
N = N+ i
( 1 DN
±
N = Ni ± 1 RN
No RN
(NiDi + NoDo) Di
o
)N
(
⎡ D = ⎢1 + DN − ⎣
D = Di
D = Di
1 RN i
)⎤⎦⎥D
D = Di
N = Ni ± No
N=
characteristic diameter
characteristic rotation speed
Re =
Table 3. Correlations for the Calculation of Total Power Number (Np) of the Coaxial Mixer
Np =
μ
Ptot
Ptot
Ptot
ρ[Ni ± (No / RN )]3 Di 5
5 ⎡ ⎛ 1 ⎞⎤ ⎟⎥ D 5 ρ[Ni + (1 / DN ± 1 / RN )No]3 ⎢1 + ⎜DN − RN ⎠⎦ i ⎝ ⎣
Np =
ρ[Ni ± (No / RN )]Di 2 μ
2 ⎡ ⎛ 1 ⎞⎤ ⎟⎥ D 2 ρ[Ni + (1 / DN ± 1 / RN )No]⎢1 + ⎜DN − RN ⎠⎦ i ⎝ ⎣
Re =
Ptot ρ(Ni ± No)3Di 5
ρ(NiDi + NoDo)3Di 2
Np =
Np =
ρ(Ni ± No)Di 2 μ
power number
ρ(NiDi + NoDo)Di μ
Re =
Re =
Reynolds number
Industrial & Engineering Chemistry Research Research Note
Figure 6. Power curves of coaxial mixer consisting of Rushton turbine and wall-scraping anchor. [Note: Np1−Np4 are curves related to correlations 1−4.]
5. CONCLUSIONS
(1) The inner impeller has an obvious effect on the power consumption of the outer impeller. The power consumption of the outer impeller will decrease under co-rotation mode and increase under counter-rotation
6866
dx.doi.org/10.1021/ie4002266 | Ind. Eng. Chem. Res. 2013, 52, 6862−6867
Industrial & Engineering Chemistry Research
Research Note
(9) Foucault, S.; Ascanio, G.; Tanguy, P. A. Mixing Times in Coaxial Mixers with Newtonian and Non-Newtonian fluids. Ind. Eng. Chem. Res. 2006, 45, 352. (10) Bao, Y. Y.; Yang, B.; Xie, Y. Power Demand and Mixing Performance of Coaxial Mixers in Non-Newtonian Fluids. J. Chem. Eng. Jpn. 2011, 44, 57. (11) Guo, W. H.; Pan, J. Z.; Xu, H. P.; Tan, G. W. Numerical Simulation for Performance of Coaxial Stirred Tank. J. East China Univ. Sci. Technol. 2009, 35, 486. (12) Guo, W. H.; Pan, J. Z. Application of Computational Fluid Dynamics to Flow Research and Structure Design of Stirred Tank. Chem. Eng. 2009, 37, 20. (13) Sun, H.; Pan, J. Z. Numerical Investigation of Flow Fields in Stirred Vessels with Novel Combined Inner and Outer Agitators. J. Chem. Ind. Eng. 2006, 57, 13. (14) Zhou, G. Z.; Wang, Y. C.; Shi, L. T. CFD Study of Mixing Process in Stirred Tank. J. Chem. Ind. Eng. 2003, 54, 886. (15) Farhat, M.; Fradette, L.; Tanguy, P. A.. Revisiting the Performance of a Coaxial Mixer. Ind. Eng. Chem. Res. 2008, 47, 3562. (16) Qin, F. L. Exploration on Performance of a Coaxial Mixer with Dual Shafts in Highly Viscous Newtonian Fluids; Thesis; Zhejiang University: Hangzhou, PRC, 2012.
mode. In addition, the magnitude of the decrease or increase will be larger as RN increases. (2) The outer impeller has little effect on the power consumption of the inner impeller. Usually, the power consumption of the inner impeller in counter-rotation mode is higher than that in co-rotation mode, but the difference is very slight. The reason is that the wallscraping anchor with large diameter mainly plays the role of promoting fluid flow near the wall of the vessel, and its power consumption accounts for a relatively small proportion of the total power consumption, because of its low rotation speed. (3) Considering the impact of rotation mode, speed ratio (RN), and diameter ratio (DN) synthetically, a new characteristic diameter and characteristic rotation speed are defined. Novel correlations for the calculation of total Reynolds number and power number of the coaxial mixer can be obtained by substituting the new characteristic diameter and new characteristic rotation speed defined above for the diameter and speed in the classical formulas of Reynolds number (Re) and power number (Np). By comparison, the results calculated by novel correlations can reflect the high efficiency and low power consumption of the coaxial mixer better.
■
AUTHOR INFORMATION
Corresponding Author
*Tel.: 13588807052. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was financially supported by the Fundamental Research Funds for the Central Universities (2012QNA4018), the Specialized Research Fund for the Doctoral Program of Higher Education (20100101120031), and the National Natural Science Foundation of China (21206144).
■
REFERENCES
(1) Ding, W. Y.; Wang, Y. C.; Gao, Z. M.; Shi, L. T.; Liu, Q. Study on Mixing Characteristics of Multiple Impellers in a Stirred Tank. J. Chem. Eng. Chin. Univ. 1999, 13, 352. (2) Xie, Y.; Bao, Y. Y.; Liu, T.; Zhang, Z. D.; Gao, X. H. Power Demand and Mixing Performance of Coaxial Mixers in Newtonian Liquids. Chin. J. Process. Eng. 2010, 10, 424. (3) Foucault, S.; Ascanio, G.; Tanguy, P. A. Power Characteristics in Coaxial Mixing: Newtonian and Non-newtonian Fluids. Ind. Eng. Chem. Res. 2005, 44, 5036. (4) Jiao, H. L.; Bao, Y. Y.; Huang, X. B.; Shi, L. T.; Wang, Y. Recent Research Progress in Mixing of High Viscous Fluid. Chem. Ind. Eng. Prog. 2007, 26, 1574. (5) Schneider, T.; Todtenhaupt, E. Mixing Times and Heat Transfer in Coaxial Stirrers. EKATO Ruehr-Mischtech. Chem. Eng. Technol. 1990, 62, 208. (6) Foucault, S.; Ascanio, G.; Tanguy, P. A. Coaxial Mixer Hydrodynamics with Newtonian and Non-Newtonian Fluids. Chem. Eng. Technol. 2004, 27, 324. (7) Rivera, C.; Foucault, S.; Heniche, M. Mixing Analysis in a Coaxial Mixer. Chem. Eng. Sci. 2006, 61, 2895. (8) Farhat, M.; Rivera, C.; Fradette, L. Numerical and Experimental Study of a Dual-shaft Coaxial Mixer with Viscous Fluids. Ind. Eng. Chem. Res. 2007, 46, 5021. 6867
dx.doi.org/10.1021/ie4002266 | Ind. Eng. Chem. Res. 2013, 52, 6862−6867
